Police have said they will not investigate the posting of "no snitching" leaflets through the doors of properties near the shop in south London where a 5-year-old girl was shot.

Officers condemned the action, as well as the setting up of a website urging people with information not to speak to police, but said they were powerless to act. "You're not committing an offence by putting a video up saying don't talk to the police," a Scotland Yard spokesperson said. He said the leaflets, on which the phrase "No One Likes a Rat" is written, could not be construed as threatening.

Thusha Kamaleswaran became Britain's youngest gun-crime victim when a youth fired into the open door of Stockwell Food & Wine in Stockwell, south London on 29 March. Shop assistant Roshan Selvakumar, 35, was also shot in the face. Thusha is said to be in a serious but stable condition. Kazeem Kolawoli, 18, has been charged with their attempted murders.

The "No Snitching" website shows a video with youths rapping against talking to police. Campaigns against speaking to officers are becoming increasingly common in murders linked to gang behaviour. On 29 December last year, Sylvester Akapalara, 17 was shot dead a stairwell in Peckham, south-east London. His death was also followed by "no snitch" campaign. The website, which went offline for a short while in January but is now back up, contains a graphic of a man on his knees with a gun held to his head next to the slogan "Peckham Young Gunz: We Rule in London".

The site contains a list of so-called "snitches", with photos and personal information, and invites people to "tell us about a rat". It also carries the statement: "The police are not your friend. They will say and do anything to get u to SNITCH and then destroy your life. Be smart. Don't snitch."

A spokesman from Operation Trident, which investigates gun crime, said: "Trident receives an incredible amount of vital community support. Engaging with us is not snitching but about protecting your community. Information from communities is vital to solving murder investigations and we will continue to successfully protect our vulnerable witnesses."

Kristina Gregory, Crimestoppers' youth projects co-ordinator, also condemned the campaign. "It is not about 'snitching', it's about trying to make our streets safer for us all – you, your friends and family," she said.

The "Stop Snitching" campaign has its origins in the troubled US city of Baltimore, where criminals tried to frighten people with information from reporting their activities to the police.

In 2007, a judge in Manchester ordered the destruction of T-shirts sold in an urban-clothing shop which "openly advocate illegal behaviour". They featured an armed young man pointing a gun, with the words "Gunchester" and "Snitch at your own risk". Others were emblazoned with "No snitching zone, cocaine business", and "Stop snitching, time is money".